10638 ÷ 82 
We want to divide 10638 by 82.

Going ahead to step 1:
If we divide 1 by 82, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 82

Step 2:
10 divided by 82 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Bring next digit (6) of the dividend behind the 10 and repeat the process: 106 / 82

Step 3:
82 can be fit into 106 1 times, resulting in a remainder of 24.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 82 away from 106, we end up with 24.
Fetch the next digit (3) from the dividend, attach it to 24 and continue: 243 / 82

Advancing to step 4:
The number 82 fits into 243 2 times, leaving a remainder of 79.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Deduct 164 from 243 and we're left with 79.
Take the next digit (8) from the dividend and append it to 79, then repeat: 798 / 82

Advancing to step 5:
The number 82 fits into 798 9 times, leaving a remainder of 60.
Use 9 as the next digit of our solution. 
Result so far: 129.0
Subtracting 738 from 798 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 6:
When dividing 600 by 82, we get 7 with a remainder of 26.
The number 7 becomes the next digit in our result. 
Result so far: 129.7
If we subtract 574 from 600, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 7:
82 can be fit into 260 3 times, resulting in a remainder of 14.
Put 3 as the next digit of the answer. 
Result so far: 129.73
Subtract 246 from 260 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 8:
82 goes into 140 1 times with a remainder of 58.
Use 1 as the next digit of our solution. 
Result so far: 129.731
If we subtract 82 from 140, we get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Moving on to step 9:
82 goes into 580 7 times with a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 129.7317
The remainder is 6 after subtracting 574 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 10:
82 can be fit into 60 0 times, resulting in a remainder of 60.
Put 0 as the next digit of the answer. 
Result so far: 129.7317
The remainder is 60 after subtracting 0 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Moving on to step 11:
When dividing 600 by 82, we get 7 with a remainder of 26.
Record the quotient 7 as the next digit in the result. 
Result so far: 129.731707
If we take 574 away from 600, we end up with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Going ahead to step 12:
The number 82 fits into 260 3 times, leaving a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 129.7317073
If we take 246 away from 260, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 13:
The number 82 fits into 140 1 times, leaving a remainder of 58.
Use 1 as the next digit of our solution. 
Result so far: 129.73170731
Deduct 82 from 140 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

The final result is 129.73170731 with a remainder of 5.8e-08.